can u answers dis?

Question

If the length of a rectangle is increased by 3 cm and its width by 8 cm its area will be increased by 255 cm². If its length is increased by 8 cm and its width by 3 cm its area will be increased by 200 cm². Find the dimensions of the rectangle.

Answer 1

(x+3)(y+8)=xy+255
(x+8)(y+3)=xy+200

xy+8x+3y+24=xy+255

xy+3x+8y+24=xy+200

8x+3y=231

3x+8y=176

11x+11y=407
x+y=407/11
x+y=37

3(37)+5y=176
111+5y=176
5y=65
y=13

x+13=37
x=24

24cm by 13 cm
im really bored

Answer 2

Let the dimension of the rectangle be L and W

L x W + 255 = (L + 3)(W + 8) ... (1)

L x W + 200 = (L + 8)(W + 3) ... (2)

Take (1) - (2),

55 = (L + 3)(W + 8) - (L + 8)(W + 3)

LW+3W+8L+24 -LW-8W-3L-24 = 55

5L - 5W = 55

L - W = 11

L = W + 11 ... (3)

Substitue (3) into (1)

(W + 11) W + 255 = (W+14)(W + 8)

W^2 + 11W + 255 = W^2 + 22W+112

11W = 255-112

11W = 143

W = 13

Substitute W =13 to find L,

L = 13 + 11 = 24

Hence the Length is 24 cm and the Width is 13 cm

Answer 3

Croasis has given you the right answer but you need to figure out how to solve these problems on your own. Read the word problem several times making sure you understand what it says. Next, try to write down simple mathematical sentences. In the very first sentence you get a clue: it talks about length, width and area. The area of a rectangle is length*width = area. So now what? It does not give you the lengths but does provide quantities of increase for length, width and area. Okay, so we can write:
(length+3)*(width+8)=area+255. We do the same for the second sentence:
(length+8)*(width+3)=area+200. So now we have two simultaneous equations that we can solve. When you solve these equations you will notice that any term that has length*width can be replaced by area. Why? Simple: area=length*width as we stated in the beginning. Now go and see how Croasis has done it. Word problems become easier as you practice. In fact, they are addictive because you end up having fun. Enjoy!

Answer 4

Present area is length times width = LW

From the first statement

(L + 3)(W + 8) = LW + 255
LW + 8L + 3W + 24 = LW + 255

Subtract LW and 24 from both sides

8L + 3W = 231

From the second statement

(L + 8)(W + 3) = LW + 200
LW + 3L + 8W + 24 = LW + 200

3L + 8W = 176

Now we have 2 equations in 2 unknowns

1) 8L + 3W = 231
2) 3L + 8W = 176

One way to proceed is to multiply equation 1 by 8 and equation 2 by 3

64L + 24W = 1848
9L + 24W = 528

So we can subtract the equations and end up with one equation in one unknown

55L = 1320
L = 24

Substitute this result into equation 1

8(24) + 3W = 231
192 + 3W = 231
3W = 39
W = 13

So L = 24, W = 13

Check this using equation 2

3(24) + 8(13) = 176
72 + 104 = 176
176 = 176

So we are completely happy with our answer - isn't this fun?

Answer 5

(l + 3)(w + 8) = lw + 255
lw + 8l + 3w + 24 =lw + 255
8l + 3w = 201

(l + 8)(w + 3) = lw + 200
lw + 3l + 8w + 24 = lw + 200
3l + 8w = 176

5l - 5w = 55
l - w = 11
l = w + 11

3(w + 11) + 8w = 176
3w + 33 + 8w = 176
11w = 143
w = 13

l = 13 + 11 = 24

The dimensions are 24 cm and 13 cm

Answer 6

say the original sizes are l and w.

(l+3)(w+8)=l*w +255
l*w+8l+3w+24=l*w +255 so after simplification
you have the equation

8l+3w=255-24=231

Similarly,

(l+8)(w+3)=l*w+200

leads you to

3l +8w=200-24=164.

can you solve the linear system?

Answer 7

(x+3)(y+8) = xy+255

or 8x+3y = 255

(x+8)(y+3) = xy+200

or 3x+8y = 200

Solving, x = 26.18, y = 15.18

Answer 8

I did it myself! and got 13 X 24 like other answerers who so diligently showed you ALL the work

Answer 9

ifn i wuz bak in skul i betcha i cuk prully anser dat. but momma sez da madula oblongodda is whut makes der gaterz means sos im nut gunna ansers.

Answer 10

Use differentiation.